Math notation discussion.. Skip Skip Cave Cave Consulting LLC
---------- Forwarded message --------- From: Computing Education Research Blog <[email protected]> Date: Thu, Dec 13, 2018 at 5:09 PM Subject: [New comment] Fixing Mathematical Notation with Computing, and "Proving" It with Education To: <[email protected]> orcmid commented: "The original "A Programming Language" and related developments of APL and it successors represent a kind of tour de force. There's no doubt about it. I do think we need to be careful. The work on notations for computation is a bit different than math" Respond to this comment by replying above this line New comment on *Computing Education Research Blog <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=http%3A%2F%2Fcomputinged.wordpress.com&sr=1&signature=09b7d337306771e189e3a7ddda4c6784&user=1acafc4e7428fb53016b8bbc38fa8a03&_e=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&_z=z>* <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=http%3A%2F%2Fcomputinged.wordpress.com&sr=1&signature=09b7d337306771e189e3a7ddda4c6784&user=1acafc4e7428fb53016b8bbc38fa8a03&_e=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&_z=z> <http://gravatar.com/orcmid> *orcmid* commented <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fcomputinged.wordpress.com%2F2018%2F11%2F02%2Ffixing-mathematical-notation-with-computing-and-proving-it-with-education%2F%23comment-65811&sr=1&signature=48fd823df6a45c0880f4d86e805f85bf&user=1acafc4e7428fb53016b8bbc38fa8a03&_e=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&_z=z> on Fixing Mathematical Notation with Computing, and "Proving" It with Education <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fcomputinged.wordpress.com%2F2018%2F11%2F02%2Ffixing-mathematical-notation-with-computing-and-proving-it-with-education%2F&sr=1&signature=0341695fbdc365de1387c5f13a06c749&user=1acafc4e7428fb53016b8bbc38fa8a03&_e=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&_z=z>. in response to *Mark Guzdial*: I was looking for a paper that I needed to review last night, and came upon these paragraphs in the paper I brought up by mistake. This is bold language: It might be argued that mathematical notation (MN) is adequate as it is, and could not benefit from the infusion of ideas from programming languages. … Continue reading “Fixing Mathematical Notation with Computing, and “Proving” It with Education” <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fcomputinged.wordpress.com%2F2018%2F11%2F02%2Ffixing-mathematical-notation-with-computing-and-proving-it-with-education%2F&sr=1&signature=0341695fbdc365de1387c5f13a06c749&user=1acafc4e7428fb53016b8bbc38fa8a03&_e=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&_z=z> The original “A Programming Language” and related developments of APL and it successors represent a kind of tour de force. There’s no doubt about it. I do think we need to be careful. The work on notations for computation is a bit different than mathematics, and thinking of the computational notation as one to be brought to mathematics strikes me as a misunderstanding of what mathematics is all about and the connection with computational systems (as applied mathematics in some sense). The semantics of APL is not mathematical, it is computational. I wonder if the desire to provide mathematical notation in programming languages, a laudible accomplishment at the time, now seems to have led to some confusions about which is what. Having the same notation might not be a great idea if it means the difference becomes even more confused. 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